Give a reason for each statement: a) Q1 = T, b) Q2 = P2

Here are the reasons and proofs for the given statements:

2.1 Give a reason for each statement.

• a) Statement: $\hat{Q_1} = \hat{T}$

  • Reason: Tangent-Chord Theorem. The angle between the tangent PQ and the chord QT ($\hat{Q_1}$ or $\angle PQS$) is equal to the angle in the alternate segment ($\hat{T}$ or $\angle QTS$).

• b) Statement: $\hat{Q_2} = \hat{P_2}$

  • Reason: Angles in the same segment. In the cyclic quadrilateral PQRS, angles $\hat{Q_2}$ ($\angle RQS$) and $\hat{